Nitrous oxide (N(2)O) and methane (CH(4)) are chemically reactive greenhouse gases with well-documented atmospheric concentration increases that are attributable to anthropogenic activities. We quantified the link between N(2)O and CH(4) emissions through the coupled chemistries of the stratosphere and troposphere. Specifically, we simulated the coupled perturbations of increased N(2)O abundance, leading to stratospheric ozone (O(3)) depletion, altered solar ultraviolet radiation, altered stratosphere-to-troposphere O(3) flux, increased tropospheric hydroxyl radical concentration, and finally lower concentrations of CH(4). The ratio of CH(4) per N(2)O change, -36% by mole fraction, offsets a fraction of the greenhouse effect attributable to N(2)O emissions. These CH(4) decreases are tied to the 108-year chemical mode of N(2)O, which is nine times longer than the residence time of direct CH(4) emissions.